Question

What are Quantum numbers? Explain the quantum number in brief.

Answer 1

Hint: The Quantum numbers are a set of rules that can describe the trajectory and the movement of an electron in an atom. The values of the conserved quantities of a quantum system are defined by the quantum numbers. There are four quantum numbers.

Complete step by step solution:
Let us start with what are Quantum numbers.
The Quantum numbers are a set of protocols that are used to describe the position and energy of an electron in an atom.
These are a group of numerical values which provide solutions that are acceptable by Schrodinger wave equation for hydrogen atoms.

There are four quantum numbers. These can completely describe the trajectory, position and energy of an electron in an atom.
a.) Principle Quantum number
b.) Azimuthal Quantum number
c.) Magnetic Quantum number
d.) Spin Quantum number

Now, let us see all these one by one.
a.) Principle Quantum number
It is denoted by ‘n’. It tells about the principal shell of the electron. It describes the probable distance between the nucleus of an atom and the electrons. The value of ‘n’ can be any positive integer. So, n = 1,2,3,4,5,6 etc.
b.) Azimuthal Quantum number
It is denoted by ‘l’. It is also called orbital angular momentum quantum number. It describes the shape of the orbital. Its value starts with one less than the principal quantum number. Its value is -
‘l’ = (n-1)
c.) Magnetic Quantum number
It is denoted by ‘${m_l}$’. It determines the total number of orbitals in a subshell and the orientation of these orbitals. The value of the magnetic quantum number depends upon the value of the azimuthal quantum number. Its value ranges from -l to +l.
So, ${m_l}$ = (-l) to (+l)
d.) Spin Quantum number
It is denoted by ‘${m_s}$’. This value tells the direction of the spin of the electron. The possible values of spin quantum numbers are $ + \dfrac{1}{2}$ and -$\dfrac{1}{2}$.
The positive value of spin means the upward spin while the negative value means the downward spin.

Note: The value of Azimuthal quantum number is equal to the total number of angular nodes in the orbital. The value of the spin quantum number is independent of principal, azimuthal and magnetic quantum number. It is never possible that two electrons in the same orbital will have the value of all four quantum numbers the same. If they have the same value of three quantum numbers, the spin magnetic quantum number will have different values.